Reentrant network



Feb. 13, 1940. NALFQRD. 2,190,131

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A. AgFoRl 'RENTRANT NETWORK Filed Jan.` 2. 193712` a sheets-sheet' a .mw-:mon Y afwas-WAUW@ ATTORNEY Patented Feb. 13, 194()v UNITED STATES PATENT OFFICE aEnN'rnANT NETWORK Andrew Alford, New York, N. Y., assignor to Mackay Radio and Telegraph Company, New Fork, N. Y., a corporation of DelawareA Application January 2,' 1937, Serial No, 118,886

l'lClaims. (Cl. 178-44) from a source of high frequency alternating current to a load. The reentrant network may be a simple section of single conductor ortwo conductor line similar to the main single conductor or two conductor liney in which it is inserted, the ends of this section being connected together to form a closed loop. The energised part of the f main transmission line Joins into this loop at some point of its circumference. The passive part of the main', transmission line branches from this loop at some other point of its circumference. The loop introduces lreflections in any waves transmitted over the transmission line in which it is inserted end'mediiies the transmission of waves along that line. The magnitude and/or phase of the reflections land the modifications in transmission depend on the circumference ofthe loop in terms of wavelengths and on the relative positions around the loop of the two points of so junction with the main line. In certain special cases the circumference alone or the relative position of the junction points alone is controlling.

provide a structure which maybe used variously as a highly efiicient transformer, lter or phase shifting device. Another object is to provide such ing distributed constants as'` distinguished from lumped impedances.l Another feature of the present invention is that it provides a tn `influencing network whose dissipation is ordinari- `50 ly exceedingly low, thus giving. low losses when ,the network is employed as a' transformer and giving low losses and sharp cut-oi! characteristics when the device is employed as a filter. Furthermore, my invention provides a filter whose char- 55 -acteristicsresult in a even if in A principal object of the present invention is to special circumstances the dissipation is comparatively high.

It is another object of the present invention to provide a transmission modifying network which shall be conveniently adjustable and which shall 5 have sufficient ldegrees of freedom so that it may be flexibly adaptedto widely different conditions.

Although in the simplest applications of my invention the network is connectedln a transmission line between a source of alternating current 10 y and a useful load to which the alternating current energy is to be delivered, it is also contemplated that the network may be connected between any live circuit such asa circuit containing both the source of alternating current energy and l5 the useful load to which said energy is to be delivered and any passive circuit, which need not be truly a load in the ordinary sense. This passive circuit may for example, be a non-dissipative impedance whose function is to modify the distri- 2o vbution of energy inthe live circuit. In such a case my network serves the purpose of modifying the inuence which the non-dissipative passive circuit exerts upon the live circuit.

The invention may be more clearly understood 25 Atrant network is connected between a source of l alternating current and a load. Fig. 1A repre- 30 sents one particular detailed structural form of m Fig. l.

Figs. 2, 3 and 4 represent alternative embodiments of my invention in which the network is connected similarly to Fig. 1 butin which diifer- 35/ ent types of transmission line are employed.

Fig. 5 represents an alternative form of Fig. '1 in which a transposition is used to replace a 180 length of line.

Fig. 6 schematically represents an arrangement 4o whose structural form may be like any one of Figs.

l, 2, 3 or i but whose load is assumed to be matched to the surge impedance of the line.

' Fig. '7 schematically represents an arrangement whose structural form may be like any one of Figs. 1,2. 3 or 4.

Figs. 8 and 9 are sets of curves which represent the intensity and position of the standing waves insuch a vspecial circuit as Fig. 6 and which may be used for determining the influences exerted on the transmission and/orreflection of4 waves by any of the networks in accordance with myinvention.

Fim-10i: afamilyofcurveswhichmaybeused in determining the influence of a network in 56 accordance with my invention, particularly when such a network is employed as a'rejection filter.

i Fig. 11 'represents a further set of curves which may be useful in the preliminary design of a network in accordance with my linvention especially when the network is intended to reject a certain predetermined frequency and pass or reject certain other predetermined frequencies.

Figs. 12, 13 and 14 represent schematically certain embodiments of my invention in which the reentrant networks serve as filters connected between sources of alternating current. energy ple, parallel two-wire transmission line 03, |04. 4At an intermediate point in this transmission line a reentrant network is inserted which comprises the two limbs i05 and 06. These two limbs are composed of sections of transmission line having the same characteristics as the transmission line H03` and are. generally of different lengths A and B respectively. For convenience in notation the total perimetral length around the reentrant network, that is, A+B, will be represented by u vwhile the difference in the Alengths of -the limbs of the reentrantnetwork, which for-deiniteness is considered to beA-B even if B is larger than A, will be represented by v. I

IThe lengths A land B of the limbs of the network, as. well as the derivedlengths u and v, are measured in. degrees with respect to the frequency under consideration, the. wavelength of traveling waves of this frequency along the 'transmission line being taken as 360. that this wavelength is twice the distance be.-

. tween successive peaks of standing waves, and is equal to where c' is the velocity of propagation ofthe traveling' waves `along the transmission line. The above interpretation of the lengths A, B, u, and-v is used throughout the specification. f

The structure shown in Fig. 1 is illustrated in u vgreater detail in Fig. 1A which shows one particularly advantageous type of construction. This construction enables the reentrant network to be effectively associated with an existing transmission line without cutting the line. Also this construction permits the dierence v in the lengths of the limbs A, B of the reentrant network to 'be readilyadju'sted Without altering .the position of junction points |20A and withoutaltering the total circumference u of the network.

The network of Fig. 2 is construct'eelof twowire transmission linegof the concentric type. This type of line is well known. The network" of Fig. 3 is made up of rubber insulated two-wiretwisted pair. This twisted pair may be ordinary lamp cord but for high frequency transmission it should preferably be slightly modied'either by omitting the textile layer usually served on the It willbe noted If, however, the attenuation coelfcientk issumwire under the rubber insulation or by employing a very non-hygroscopictextile or paper for this layer. Also the rubber should be free from hygroscopic fillers or other materials which increase the high frequency losses. If an outer textile braid is provided over the rubber it is advantageous to varnish this braid or impregnate it with a water resisting compound.

The network of Fig. 4 is built of single-conductor line and is connected in a single-conductor line which might be employed for example, in feeding an antenna.

Although these various constructions diier in structure and in their practical applications, they may be treated together as regards the electrical theory .of their reentrant networks. Thus, unless certain forms are specifically excluded, the analysis given hereafter may be considered as applying to any ofthe structures of Figs. 1, 2, 3 and 4 as well as to polyphase or single-phase multipleconductor lines and to structures comprising different types of lines in the different branches.

The schematic representations of Figs. 6, 7, 12, `13 and le also are to be understood as representing structures built of any type or ty-pes of singleconductor or multiple-conductor transmission line, although for simplicity the line is represented by a single line in these gures. necessarily complicating the formulae and rules of dimensioning, these formulae and rules have ben derived on the assumption that all sections of line in one system have the same impedance different characteristics are within my invention and may, in special cases, be advantageous. y

For simplifying the preliminary explanations reference will rst be made to Fig. 6 which schematically represents an arrangement similar to any one of Figs. l, 2, 3 or 4, excepting that the load 602 is an impedance whose value is the same To avoid unas the surge impedance of the transmission line $03-$04. The influence exerted by network 605-606 upon the transmission between this transmitter and load can be described in terms of the vectorreflection coefcient Reif of the net-y work and its vector'transmission coemcient Gels. These vector coelcients have the .ordinary accepted signicance and refer to the voltage wave,

ciently small so that it may be neglected for the frequencies of waves andlengths of wires under -I consideration, the above formulae may be conslderably-siml'iliiied- Setting k equal to zero and separately expressing the absolute magnitudes R v' G and their vector angles r and a respective-f ly,weobtain l.

4+cos vcos u the'following auxiliary equation cos r Ai4-cos vcos u Those lcoeillcients It, r,.,G and y denne the elec- 20 trical effects of a loop network according to my inventionin terms of reection and transmission regardless o f whether the line in which the loop \is connected contains other points of reection or not.l Ithowever the system which contains the network is a simplified arrangement such as shown in-Fig. 5, then these coefficients may be very simply interpreted to directly represent the waves traveling 4in lines 603 and 604. Assume for example that the total forward wave entering the network 605-606 has a unit amplitude and a zero phase at 'the terminals BID, then the total backward wave along line '803 is Re. Also the total forward wave along line 604 is Gei. These phases refer respectively to the phase of the wave as it leaves terminals 6W and -620 and are measured with respect tothe phase of the forward wave incomingto the network at terminals M0.

Even when the network is connected in some more general arrangement than that of Figi 6 Geil and Re represent-the transmission and reilection coefficientsv in the usual manner, though l the above described simple relationship between these coefilcients and-the .total forward and backward waves vno longer holds'.

If we consider as standing waves not only those pure standing waves whose minima are zero but also those. whose minima have definite values,

' we may find it convenient to denne the ratio of 50 the maxima and minima. For any standing measured at the voltage antenodes, `to the mini--l mum r. m. s. voltage, measured at thevoltage nodes, is, hereinafter rcalled the "standingwave ratio or .Q ratio of the wave and isdesignated.

by Q f v Because of the greater facility with which standing waves can'be measured it is for many purposes more convenient to .define the properties 'of a reentrant network in terms of standing waves ratherthanl by its reection and transmis sion coeiilcients--which referto traveling waves or traveling wave components. Use is therefore made of A two auxiliary) coemcients Acalled the natural standingwave ratio of the network andy the natural'position parameter of the network. These characteristics of any network may most conveniently be denned by supposing that the vnetwork is connected in an arrangement such as shown in the surge impedance of the tron line. In this arrangement. which is assumed for analy- A sis, therewill be no reflections from the load "2 and hence no standing waves in the line lll. In general. however, there will be standing waves in eachofthelimbsili and t andalsostanding standing waves 623 in Fig. 6

ywave ther'atio of the maximum r. m. s. voltage,

Fig. 6in which the load is matched to waves, as represented byv curve 623. in line 603. The ratio of the maximum r. m. s'. voltage tothe minimum r. m. s. voltage of standing waves $23.*

which is the Q ratio of waves 623, will hereinafter l be known as the "natural standing wave ratio of the network and will be designated 'by the letter P.. Also the distance from a voltage maximum of these standing waves '623 to the terminals GIU will hereinafter be known as the "natural position parameter of the network and will be designated by the letter p. These natural coemcients P and p are characteristics of the network itself,

and may be referred to even when' the network is connected in some more general arrangement than that shown in Fig. 6. In such a case, however, P or p will still represent the standing wave ratio (I.)v or position length q of the waves which would be produced in such an ideal arrangement as Fig. 5 and should not be taken to represent the Q ratio or'position coefllcient of the waves which are actually produced in the more complex v arrangement wherein the network happens actually to be connected.

Since the value of Q of the waves I!! in the special arrangement of Fig. 6 is equal to -1R the natural standing wave ratio for any networkl Similarly since the position coemcient q of the the natural position coefficient ofthe network is Vwork. the diilerence in lengthw between the limbs of theinetwork being kept constant for any onecurve. From these curves it is possible to find the value of P for any given values of thedimensionsu and v. Similarly the curves of Fig. 9 and Fig. 9A show the variations of p with the variations of the perimeter u, v again being kept constant for any one curve. From this familyl of curves vit is, therefore, possible to find the value of p for any given values of network dimensions 'u and v.

Conversely any desired value of -P may be obtained by properlyadjusting the dimensions u and v. For example, to lobtain a value of 7.0 for 'P inany network we may dimension the network v=100; or so that u=33 and 'o=100, etc.'

of. Fig. 8 butare drawnto' a larger. scale. By

interpolation aninnnite number of such primary sets o fdimenslons can be obtained. Furthermore, each of the sets of primary values obtained from these'curves or from interpolation has associated with it an innite number. of equivalen values. For example.- in the first set of primary values given above u='12l, v=90".` there'may be used for u any one ofthe values 121, 239. 481. 599'. 841, etc., obtained from Nx360r1219f and similarly there may be used for n any one of the values 90,-210,

45o?, etc., obtained :fom Nxsoo'ito. 1

' position and B=113.5.

Examining all the above sets of values for u isv equal to p; then the standing wave ratio Q and v, it will be noted that some of these sets of values are not physically realizable with real positive lengths A and B. Referring to the third primary set of values (u=33. v=100), for example, it is impossible to construct a network whose perimeter has a length of 33 and whose two limbs differ in length by 1002. In such a case use is made of one or more of the equivalent values above mentioned. Eor example, by selecting a u of 327, which is equivalent to a u of 33 as above noted, and by retaining the value of 100 for v a physically realizable setf dimensions is obtained. Such a network would, for example, have a length, A, of 2l3.5 and a length, B, of 113.5?. However, a great number of the structures which may be read off directly from the curves, including many of the-best ones from a practical standpoint, are physically realizable without any replacement of u or v by equivalent values. For example, the first set of primary values previously mentioned (u=121, o=90) is physically realizable. Generally the region to the right of the small circles in Fig. 8A represents sets of Values which are physically realizable without resorting to equivalents.

There is another set ofv equivalent .structures which may be obtained by the use of a transposition in one of the limbs of the reentrant network. Since a transposition in any limb is equivalent to a delay of 180 it is possible to shorten the length of some of the structures by replacing 180 of physical length by a transposition.

For example, the structure referred to above in which A=213.5 and B=113.5 may be replaced by a structure in which A=33.5 with a trans- A structure which includes such a transposition but which is otherwise similar to Fig. 1 is illustrated in Fig. `5. The use of a transposition is particularly applicable to networks built of two-wire linel such as shwnin Eig-.11, and .to twisted wireline Such as shown in Fig, 32 Other` phase changing" means may also be employed to replace part of the physical length of the network, but the transposition is particularly desirable because'of its simplicity and its freedomirom reflections at all frequencies.

In one very useful embodiment of my invention a reentrant network as illustrated .in Fig. 1 serves, in conjunction with certain portions of the transmission line 10S-104, as a transformer. In this figure, 10 l4 represents a transmitting equipment; 103-104 a transmission linerconnecting that transmitter with a load 102 and 10S-106 a network inserted in this transmission line. If

`the load 102 is not exactly matched to the surge impedance of the transmission line there will be standing waves 124 dependent on the mismatch q'by the load-be represented 'by' L. l'The natural standing-wave ratib and the natural position parameterl'of the network' are P`and p. Now the network may-be positioned along the transmission line so that'the distance between its terminals 1120 and a voltage peak of standing waves 124 the load to the line.

of waves 103 will be equal to whichever is larger. Alternatively the network may be positioned so that the distance between its terminals and a voltage peak of wave 124 is equal to P|90 in which case the Q ratio of waves 123 will be equal to PL.

If it is desired to give waves 123 a smaller standing wave ratio than waves 124, the first mentioned location of the network must be used. On the other hand, if it is desired to give waves 123 a very high standing wave ratio, the second mentioned position may sometimes be more convenient.

In the most usual application of this embodiment of my invention the network 105-106 is adjusted so that waves 123 will be completely eliminated, i. e., will have a Q ratio equal to unity. To obtain this result the network should be so adjusted that its natural standing wave ratio P is the same as L, the standing-wave ratioand the load 102 will be equal to the surge impedance of line 103.

In certain cases it may be desired to ,adjust the network so as to act as a transformer having a ratio different from that required to match In other words, it may be desired,insteadof matchingA the load to the transmission line, to introduce a deliberate amount o f mismatch for some purpose In this case it is merely necessary to express the desired mismatch in terms of the standing Wave ratio desired in waves 123. Then by the `use of the above rules for proportioning and positioning the network the waves 123 4may be caused to have the desired Q ratio.

lIn addition to its use as a transformer the reentrant network structure of my invention may also b'e adjusted to act as a cut-oir lter. In other words, the network may. be adjusted so that for one particular frequency -its natural standing wave ratio P is substantially innite.

In terms of the reflection and transmission coeiiicients this means that R=1 and G=0. The frequency at which the cut-off .takes place will be referred to as the cut-o' frequency and Willbe designated by F. At certain special other frequencies the network will again cut oir as will be more fully described in connection with Fig. 12.-

Ingeneral, however, at a frequency f, which is not the cut-01T frequency F, -the lter will transmit more or less satisfactorily.

The conditionsI for cut-o are substantially or when v= or-540?, 900 etc., and especially complete cut-ofi! occurs when boththese conditions aresimultaneously satisfied.

The cut-oil! networkshaving v=180 be' referred' to as difference. lters and the networks having u=360 will be referred toas lsum lters. The special network which hasu='360 and v=100 anduwhvich is thus` a siimfllter as ywell as a'diflerence filter will be referred to as a it is desired to, pass.

amarsi hybrid" lter. Although this hybrid filter is theoretically a sum iilter as well as a difference :filter it is, in the following discussion, considered to be excluded from each Aof these classes; thus general statements as to the properties of sum and/or difference filters arc not wconsidered as applying to thel hybrid filter unless it is specilically included.

The transmission and reection coeilicients of all these three classes of lters are given byEquations 1 and 2 as set forth above.

Fig. 10 shows a 'set of curves which directly represent the coeillcient G in terms of frequency for filters of the sumand hybrid types. In these curves the yattenuation is assumed to be .043 decibel per wave length of line (i. e., 0.0000187 decibelper 0.115 degree length of line which correspond to k=0.000013'1). 'I'his attenuation is of the order actually found in ordinary open-wire transmission lines. A simple, parallel, two-'wire line structure of number 6 A. W. G. copper clad lsteel wirewith a 12 inch spacing, for example.'

has an attenuation of approximately 1 decibel in 2000 feetat a frequency of 10 megacycles. Since the wavelength at 10 megacycles is approximately feet, this attenuation amounts to very nearly .043 decibel per wavelength. This value for attenuation, moreove will not vary rapidly with frequency because as thefrequency is increased the attenuation per foot,of wire ,also increases; at the same time the number of feet per wavelength of line becomes smaller so thatto a certainextent these two changes counteract each other. Thus, the curves of Fig. 10 fairly accurately represent the transmissions through a sum or.. hybrid alter in the neignborhooi of 'the cut-oir frequency for all frequencies between 6 and 16 megacycles. From Equations 1 and 2 it is possible to plot a corresponding set of curves for the difference and hybrid types of lters. Also similar sets of curves for sum, difference and hybrid filters may be plotted using other values of 1c than that assumed for Fig. 10. For coaxial lines the attenuation is ordinarily higher and, therefore, typical curves for this type of line would show a somewhat broader cut-ofi. For the twisted pair lines also attenuation would ordinarily behigher. I h

In the regions more remote from the cut-off point the transmission and reection coemcients.

may be reasonably accurately calculated from the approximate Equations 3, 4a, 5 and 6 instead of from the'more complex Equations 1 and 2.l Generally, moreover, in the regions remote froml the cut-off the primary interest is in the natural standing wave ratio -P since in this region the problem is one of passing another frequency r' without developing standing waves of high Q ratio, which would result in comparatively great losses. 'In' this region remote from the cut-ofi' point, therefore, Figs. 8 4and 8A serve toindicate thel behavior of the network at frequencies which If, however, it is desired to visualize clearly the pass characteristics of a given filter or if the problem of designing filters is to be facilitated it may be convenient to plot a set of curves suhas shown in Fig.411. The curves of Fig. 1l* like the curves of Figs. 8 and 8A, represent the value of the natural standing wave factor P. But instead of being plotted againstl u these curves are plotted against 'the value of frequency F (expressed in terms ofthe cut-off frequencyI F taken as unit frequency). Also, the curves of Fig'.' ll are drawn to logarithmic scale.' All the curves of Fig. 1l repre-f sent sum filters which have a u of 360 at 'the cut-off frequency F. The first four curves, respectively, represent filters whose v at the cutoi frequency is 60, 120, 180, 240. The additional curve, designated as 60+#, represents a sumlter whose perimeter has a physical length of. and whose limbs diiier in physical length by 60, the longer or the shorter limb of the 'filter being equipped with a transposition so that the eifective value of u at frequency F is 360 while the `eective value of 'v at the cut-off 'frequency F. is 240 or 120. It will be noted that the curve of the filter 60+# is very different from the curve marked 240 although at the cut-off frequency itself, both curves represent filters having a. u of 360A and a v of 240. The reason for the divergence between the two curves is, that as the frequency is varied from F the transposition whichis designated by continues to represent a fixed eiectrical length, namely 180, whereas a length of wire which at frequency F represents 180 will varyin electrical length as the frequency is changed.

It will be noted in 'general that a simple sum lter will ,cut 'off not only at the nominal cut-olf lfrequency F but also at 2F, 3F, 4F, etc. Similarly a difference lter generally cuts oi! at 3F, 1F, etc. l

l In order to' cut oif at F and yet pass `2F a sum fllter may be used having a transposition such that u=180|# and v=60+#, 0r 1L==180+`# and v=90+#. 0rl a difference lt'er'such that u=230 and v=180, or a hybrid, may be used.

If it is desired to cut oil' FA and pass 3F a sum lter with a transposition or a sum filter whose value of v is such that 3u=N360 where N is any integer, may be used.

In some cases the above described multiple cut on properly may be used to great advantage. 'Av network which is particularly useful for passing frequency f while suppressing the principal harmonics of f, for example, can be constructed by making u=180 and v=60 at frequency f.

vimpedance looking into such networks at the cutoff frequency is 'extremely large in comparison with the surge impedance of the line. This property is independent Aof the value of v of the particular lnetwork and is a characteristic of hybrid networks and of all sum networks with one exception, namely, those which have v=0, 360, etc. Such networks are not cut-0E networks at all.

The filter networks of my invention may be used for a variety of purposes. For example, Fig- 12 shows a system in which two high vfrequency transmitters l20| and l20l', working on two different frequencies f and f', are connected to the same antenna |202. In this figure reentrant networks H05- i206 and i205 and i206' are utilized for the purpose of minimizing the interference between the twoV transmitters. Network |205- .I206 is designed so that its perimeter u equals .360 at frequency f delivered by transmitter l20|'while network |205'-I206-is de- Sighedso that its perimeter is equal to 360 at frequency ,f delivered by transmitter |20l. 'I'hus reentrant network H05-|206 does not allow frequency ff delivered by transmitter i20i' to enter interference with one another.

transmitter i20i. At the same time, however, this network passes frequency ,fA coming from transmitter I20I wtihout unduly serious reections. A matching network schematically represented by I2 I5 is placed between the transmitter .and the network I205-I 206. This matching network is designed and positioned according to the principles `previously explained so as to match the surge impedance of transmission line I2 Ili'to the impedance resulting at terminals I2 I 0 of network |205| 203 at the frequency f of transmitter l 20|. Similarly reentrant network I 2I5' matches the impedance resulting at terminals I2 I0' of network |205'-I206' tothe surge impedance of the transmission line IEM'.

'I'he distance between network I 2I5 and network H05-.|206 will, in accordance with the rule previously given for .positioning matching networks, be simply the natural position parameter p of network |2I5 plus the natural position parameter p of network |205-I206 both computed with respect to frequency f. Preferably network |2|5 is designed so as to also to actas a cut-off filter for frequency f thus providing double filtering. Usually thisV is most conveniently accomplished by making networks I2I5 and H05-|206 identical to each other. In this case the distance between these networks will be twice the natural position parameter p of' either network at frequency f. Similar considerations hold with respect to networks |2|5 and |205'-|206.

The distances: should be such that at frequency f the impedance of line |204, with all the structure connected to it, will be substantially infinite as seen fromjunction point |250. If network 0, 180, 360, etc. If, however, this network is a dierence filter the natural position parameter p of the network at frequency f' must be com-v puted. Then :c should equal this p, or should exceed it by an integral number of half wavelengths.

Fig. 13 shows an arrangement similar to that of Fig. 12 except that one of the transmitters has been replaced by a receiver. The networks |305|306 and |305-I306' enable simultaneous operation of the transmitter and receive without Or either may be used individually.

The networks utilized'in such arrangements as shofwn in Figs. 12 and 13 should bedesigned in such a way that the standing waves which they cause at the transmitted frequencies are not so intense as to cause either great losses due to circulated currents or undue voltages on the various limbs of the networks or in lines |203 and |203' or |303 and |303'. 'I'hat is, the designof network |205-I 206 should be such that the standing waves in line section |203 have a suiiiciently low Q ratio.

In order to avoid the danger of rise in voltage and current along the section of transmission line |2|0 it is desirable to select the constants of'network H05-|206 in such a manner that the amount of reflection at its terminals at the passing frequency-is relatively small. In practice,V

however, I have'found that standing wave ratios of the order of 7 or lower are entirely practical.

' By means of curves like those of Figs. 10 and 11 it vis possible to choose for any given frequency ratio vline |303'.

mustbeeiected..

For example, in network |305-I 306 the amount of ltering which is required is usually not nearly as high as would be required in network |305|306'. On the other hand, in line section |303 the standing wave losses would be of more moment than the losses inthe section of Thus in actual practice the network ISBW-|306' would usually be designed so as to have maximum or nearly maximum cut-off and With only minor regard to the standing waves and the losses which result therefrom online |303', ai

while network H05-|306 in the same arrangement would be designed to provide a less complete nected over line |433 to a radiating antenna |434. A small portion of the energy delivered to line |433 by amplifier |432 is diverted into the branch line NO3-|404 in which the network H05-|406 is connected. The current deliveredby line |404 after detection in diode |435 is passed through resistor |433. 'Ihe voltage thus developed across this resistor, after smoothing in filter |431, is applied across a portion ofthe oscil-` lator circuit suitable for controlling the oscillator frequency. .Heater |407 is connected through thermostatic control |408 to a. source of power I 409.

The operation of the device of Fig. 14 is as follows: The reentrant network is adjusted so that the perimeter u is nearly equal'to 360 at the assigned frequency of the oscillator, preferably so that the frequency which is cut 01T by the network is slightly different from the assigned frequency of the oscillator, for example, just below this assigned frequency. The heatingwires |401 in conjunction with thermostat |408 maintain the temperature of the limbs of the reentrant network nearly constant so that the cutcif frequency will remain substantially the same.

I'he o of this network is made small, for example,-

30, sothat the network would be relatively compact. In accordance with Fig. l0 it may be seen that the amount which a sum lter transmits varies very rapidly with the frequency in the neighborhood of the cut-off frequency. For this reason in the arrangement of Fig. 14 the total amount of current which is transmitted to detector |435will depend in a critical manner on the frequency of oscillator |430. If the cut-off frequency of the reentrant-'network I 405-I406 lies below the normal oscillator frequency, then as the latter increases the amount of current transmitted to detector I 435 increases and vice versa. Accordingly, the direct current output of the detector which is carried by wires |438 to the oscillator 'also decreases and increases in accordance with the fluctuations of the frequency delivered by the oscillator. This direct` current which is carried by wires .|438 may be applied to vary, for example, thegrid voltage .of the ascii-- 'from 'the voltage maximaposition noted in step lator in a well known manner in order to affect the frequency delivered by it. In this manner the frequency of the oscillator may be decreased when the oscillator is drifting upward in frequency and vice versa, whereby the frequency of the oscillator may be kept substantially constant. It will be clear from the abovediscusslon that it is Fig. 15 shows a network |505|505 connected,

between a live circuit and alpassive circuit. The

live circuit comprises source connected over i line |540 to load |54|. The passive circuit comprises reactive impedance |502 which dissipates. no power and is therefore not truly a load. This impedance is connected to's'ome point ofline |540 by line ISM-|504. -The networkv H05- |505 modifies the influence exerted by |502 on the waves transmitted from source |50| to load |540.

This structure is used as follows: source |50| delivers two different frequencies F, f simulta- V neously or successively. Matching device |542 is adapted to match load |54| to line |540 at fre-- quency F. This device may for example be a reentrant network dimensioned and'positioncd for simple matching at one frequency as previously explained.. vNetwork |505 is adjusted as a sum filter to cut off frequency Fso that the waves of that frequency are unaffected by adjustments of the position or length f line |504 nor by adjustments in the impedance of |502.: Line |503 is made 0, 180, 360 etc. in length at frequency F so that at that frequency line |503 will have an infinite impedance as measured at' junction |545. .Now the leng'th of-line |504 is adjusted. thus varying the impedance at frequency. f of branch |503.|504 as seen from junction |545. Also the position of junction |545 along yline |540 is adjusted. By-these two adjustments the impedance of all the structure beyond junction |545 may be matched at frequency f to the surge impedance of line |440. In other Vwords the standing waves of frequency f in that portion of line |540 between source. |50| and junction |545 maybe eliminated. This may conveniently be performed by the following steps. First the Q ratio of stand.- ing waves of frequency f in line |540 between matching device |542 and junction |545 are measured or computed. This is the Q ratio of those standing waves whichare caused by the device |542'ar`1d the load |543. The position of voltage maxima of these waves are also noted.

. Second, line |540 is cut open between junction |545 and matching device |542, and the cut end of this line isconnected to a load equal to the surge impedance 'ofy the line so to terminate the line inl a reflectionless manner. Third, the effecvarying the length of line |504 untilI thestanding measured or computed in the first step. The distance M of a voltage maximum of these standing waves from junction |545 is also noted.- Fourth, the refiectionless termination used in's'tep twois removed; the cut line is reconnected; the junction point |545is adjusted so that its distance Expressed in other jugate net one is M as measured in step three. 2 Now it will be found that there are substantiallyl no standing waves between junction |545 and source |50| either at frequency F or fre-- quency f. If it is desired to stillv further reduce any slight standing waves that Vmay be present `the perimeter u of loop |505|505 may be slight- 1y changed to eliminate the standing waves of frequency F, and then the length of line 504 and/or the position of junction |545 may be slightly adjusted to eliminate waves of frequency f. The impedance |502 is preferably a short cirf i cuit. The length of line |553 is preferably zero.

Qne reentrant network may be used to neu-a tralize standing waves caused by another `reentrant networkfin the same wayin which areenf.trant network may be used'as a matching transformer to match the impedance of a load tothe surge impedance of a line, ire., to eliminate the standing'waves caused by a mismatched load.

Such arrangements have already been described in connection with Figs. 12 and 13 in which at least one of the two mutually neutralizing" networks served as a nlter for cutting on an unwanted frequency. Such a pair of networks which mutually neutralize eadh others reilectors at some given frequency is' hereinafteureferred to as 'a conjugate Vpair with respect 2 that frequency. words' a conjugatepair of net-l works is a pair which isconnected in a reflectioniess line like that of Fig.' 6 would cause no reflections except inside the'fnetworks themselves and in the section of line between them'.-

Two networks are coniiisatc if the Pof one equals the P of the other and if the distance along the line between the closest terminal of the network is equal to the pf of one network plus the p of the other.' Since the conjugacy of two networks depends not only on the dimensions -of the networks but also on theirrelative position it will be useful to consider the jtwo networks of a conjugate pair together with the section-of line between them as a unit having for two conductor lines two input terminals and two Ioutput terminale. or in the case of single conductor line.' one input and one 'output terminal. Such a coinplete unit will be called a -complete conjugate ne lA complete coniugate net may be used to change phase of forward or backward traveling waves without changing the magnitude of thesev waves. The total phase delay dueto insertion of.. a complete conjugate net is minus the length j of the section of line which joins the two4 reen-'gy'. trant networks and together with themconf stitute the complete coniugate net. .In .itl'rer words if we call the-insertion delay D and represent the natural ,position parameters. p ofv the component reentrant networks by pr and pa, then trant networks are applied to a line without cutting the ,line as shown in Fig. 1A. In' sucha A complete conjugate net may also be used -to introduce a desired amount of reection at one frequency without introducing any reflection at the frequency for which it is conjugate. The complete net taken as a whole may be considered as a unit which has a natural standing wave ratio P and a natural position parameter p of its own. I'he P and p of the complete network will be designated by P3 and p3 respectively; the P and p of the component network which is nearest to the source will be designated by P2 and p3;

which the P and p of the other component network which is nearest the load or passive impedance may be designated by P1 and p1. The distance between the nearest terminals of the component networks is designated by S. All distances are in degrees at the frequency under consideration which is usually not the conjugate frequency.

.P.=w+/w21 where w is given by cos (2S-2pr-2p1) the quadrant of m being such that sin4 m has the same signv as sin (ZS-Zpz-Zp A complete conjugate net which is conjugate at I frequency F and which has a desired Pa at frequency f may be substituted in Fig. 15 for the branch line'. |503-I504 containing network |505-'I56- The complete net is inserted in series in line I 540, which can actually be accomplished without cutting line |540. Because-of the conjugacy at frequency F the matching which has been effected at that'frequency by device |542 is not disturbed. Yet by adjusting the P3 of the complete net at frequency f matching may be effected at this frequency in accordance with the rules previouslyexplained for matching by means of a single reentrant network.

For the various applications of reentrant networks according to my invention the waves .circulating around the reentrant loops themselves may, in exceptional cases, considerably exceed the waves in the main transmission line, thus making it desirable in some cases to consider these l waves. 'Ihe fraction H of the total transmitted power which is dissipated within the loop is given H=1A+R2G2- 9) This fraction H may be evaluated' in any given case by computing the values of G and R from account of attenuation by replacing y' by i-Hc in the equations as above Written. It should be noted that the actual maximum voltages in the limbs may be far lower than the limits a and b if it happens that a voltage peak does not fall Within each limb. Also if the atenuation is appreciable the actual maximum voltages will usu- -ally be slightly lower thanthese limits even if Equations 10 and 11 are corrected for attenuation. By use of Equations 93 l0 and 11 it is possible to avoid so dimensioning the reentrant networks of my invention, that intolerable potentials or power losses occur in the networks.

in connection with the preceding description it should be understood that the sources and loads may be interchanged in accordance with the well known reciprocity rule. For example, in Fig. 12 the radiating antenna may be employed as a collecting antenna and the two transmitter equipments may be replaced by receiver equipments having the same terminal impedance.

While I have described particular embodiments of my invention for purposes of illustration, various modifications and adaptations thereof, occurring to one skilled in theart may be made within the spirit ofthe invention as set forth in th appended claims. 1 I claim: i l. A filter network for use at a given high frequency in cooperation with a frequency line comprising a. closed loop conductor having two terminals connected to said line at spaced points thereby forming two parallel paths through said loop the sumof said paths in electrical degrees at said given frequency being 360 and the difference between said paths being other than zero electrical degrees.

2. A filter network for use at a given high frequency in cooperation with a high frequency line vcomprisinglga closedloop conductor having two terminals connected to said line at spaced points thereby forming two parallel paths throughV said loop, the difference of said paths being electrical degrees at said given frequency.

3. A highfreqency transmission circuit comprising a. two-wire transmission line, each wire of which has at corresponding points serially connected therein a closed loop conductor in such manner that two parallel paths of unequal lengths through said loop are presented.

4. A high frequency transmission circuit in acsaid loop is 340 electrical degrees at a frequency which itis desired to cut off.

5. A high frequency transmission circuit in accordance with claim 3 wherein the dierence between the two parallel paths of each loop is 180 electrical degrees at a frequency which it is desired to cut oiI.

6. A high frequency transmission circuit including a two-wire transmission line havinga cordance with claim 3 wherein the total length of matching device connected thereto for matching the impedance of the line to that of a translating device said matching device comprising a closed loop conductor connected serially between each of said wires and said translating device, `thereby forming two parallel paths through said loop, the sum of said parallel paths being other than 360 electrical degrees at the frequency for which a match of impedances is desired and the difference between said paths being other than 180 electrical degrees at said frequency.

7. A high frequency transmission systemcomprising a rst transmission line, a second trans- `mission line connected thereto, and a reentrant transmission modifying network forming two Paths. of unequal length operatively associated with each of said transmission lines.

8. A high frequency transmission system com- IS prising two separate sources adapted to supply a first frequency and a second frequency, respectively, a common load for said two sources, a separate transmission line for conducting energy from each lof said sources to said load, and a` 10 transmission modifying reentrant network oper- Aatively forming two paths v'of unequal length operatively associated with each of said transmission lines.v

9. A high frequency transmission system in ac- 15 cordance with claim 8, wherein said reentrant networks each comprise a closed loop conductor serially connected in said associated transmission line, thereby forming two parallel paths through said loop, the sum of said paths ofthe loop asso-` 25 frequency being 360 electrical degrees at said first frequency, the difference between the paths of each of said loop conductors being other than 180 electrical degrees at the frequency carried` by the transmission line in which it is connected. 30 10. A high frequency circuit comprising a conductor adapted to carry a high frequency current and a transmission modifying network therefor comprising a single conductor connected to said conductor at two spaced points said single conductor being longer than the part of said first named conductor between said space points.

11. A high `frequency circuit comprising a transmission line for transmitting energy from a first point to a second point and transmission 40 modifying means associated therewith comprising a second transmission line of a different length from said first line connected in parallel therewith.4 12. A high frequency circuit comprising -a co- 45 axial cable adapted to transmit energy from a .first point to a second'point and a transmission modifying means associated therewith comprising asecond coaxial cable having a different electrical length than said rst coaxial cable` and connected in parallel therewith.

13. A high frequency circuit comprising a source, a load, a transmission line connecting said source and said load. an impedance and means including a reentrant network having two arms of different length for interconnecting said impedance and said line. y

14. A transmission line adapted to carry waves of two di'erent frequencies, two closed loops serially connected in said line, the dimensions and spacing of said loops being so interrelatedthat no reections are caused at one of said given frequencies in those portions of the transmission line outside said two loops, while at the same time a desired reflection is produced at the other of said given frequencies in one of said k outsideportions of said line.

15. A high frequency circuit comprising an oscillator, an output circuit therefor, two parallel paths of different lengths adapted, to conduct energy from said output circuit toa' common 25 junction point and means for' controlling the frequency of said oscillator in accordance with the energy received at said common junction point.

16. A high frequency circuit comprising a twowire transmission line for transmitting energy from a first point'to a second point and transmission modifying means associated therewith comprising a second transmission line of difierent length than said first line connected in parallel therewith, said second transmission line .35 .having phaseshifting means therein.

' 17. A high frequency circuit comprising a twowir'e transmission line for transmitting energy from a first point to a second point and transmission modifying means associated therewith comprising a second transmission line of different length than said first ,line connected-in parallel therewith, said second transmission line having a transposition therein.

'- ANDREW A11-FORD. 45 

